Quasi-interpolations with interpolation property

Authors:
Ren-Hong Wang;Jing-Xin Wang
Affiliations:
Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People's Republic of China;Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics - Special issue on proceedings of the international symposium on computational mathematics and applications
Year:
2004

Citing 1
Cited 2

Quasi-interpolation functionals on spline spaces

Journal of Approximation Theory

Refinable interpolatory and quasi-interpolatory operators

Mathematics and Computers in Simulation
Optimal local refinable interpolants

Mathematics and Computers in Simulation

Quantified Score

Hi-index	0.01

Visualization

Abstract

Interpolation and quasi-interpolation are very important methods for function approximation. But both of them have their respective disadvantages. The interpolation function can fit the given sample points, but some oscillation may arise as in the case of the Lagrange interpolation. The quasi-interpolation function, for example, the Bernstein quasi-interpolation function, satisfies the convergence condition, but does not keep fitting the given sample points. In this paper, we present a method to construct a quasi-interpolation operator with certain interpolation property.